The Jewish people have survived for 3,500 years and we have experienced much worse than baseless predictions of a date for the “End of the World”. The destruction of our Temple and worldwide exile of an entire people was quite a cataclysm; followed by the Crusades, the Spanish Inquisition, the Black Death, the Holocaust, etc.
And yet, here we are. I am a Jew living in Jerusalem (a miracle in and of itself), son of a holocaust survivor (another miracle) actively teaching Judaism to thousands of Jews around the world (another miracle). So our attitude should be that of Alfred E. Neuman - "What, me worry?"
The Torah guarantees that there will always be Jews around observing, studying and teaching Judaism.